An efficient algorithm for incremental mining of temporal association rules

An Efficient Algorithm for Incremental Mining of Association Rules Chin-Chen Chang Department of Information Engineering and Computer Science, Feng Chia University, Taichung, Taiwan, R.O.C Department of Computer Science and Information Engineering, National Chung Cheng University, Chiayi, Taiwan, R.O.C ccc@cs.ccu.edu.tw Yu-Chiang Li Jung-San Lee Department of Computer Science and Information Engineering, National Chung Cheng University, Chiayi, Taiwan, R.O.C {lyc, ljs91}@cs.ccu.edu.tw sub-problems (1) to find all frequent itemsets, and (2) to use these frequent itemsets to generate association rules. The first sub-problem importantly governs the overall performance of the mining process. After frequent itemsets have been recognized, the corresponding association rules may be derived easily [3, 4]. Other efficient approaches have also been presented, including for example those in [1, 2, 6, 10, 11, 16, 18]. Existing mining methods cannot be applied to mine a publication-like database efficiently. A publication database is also a transaction database where each item involves an individual exhibition period [12]. Consider a publication database in Fig. 1, items A, B and C are exhibited from 1996 to 2004. However, item F is exhibited from 2002 to 2004. Traditional mining techniques ignore the exhibition period of each item and use a unique minimum support threshold. This measure is unfair for new products. Therefore, the PPM algorithm has been proposed to solve this problem [12]. Abstract Incremental algorithms can manipulate the results of earlier mining to derive the final mining output in various businesses. This study proposes a new algorithm, called the New Fast UPdate algorithm (NFUP) for efficiently incrementally mining association rules from large transaction database. NFUP is a backward method that only requires scanning incremental database. Rather than rescanning the original database for some new generated frequent itemsets in the incremental database, we accumulate the occurrence counts of newly generated frequent itemsets and delete infrequent itemsets obviously. Thus, NFUP need not rescan the original database and to discover newly generated frequent itemsets. NFUP has good scalability in our simulation. 1. Introduction Recent developments in information science have resulted in the rapid accumulation of enormous amounts of data. Consequently, efficiently managing very large databases and quickly retrieving useful information are very important. Data mining or knowledge discovery techniques are normally used to discover useful information in data warehouses. They have come to represent an important field research and have been applied extensively to several areas [7], including financial analysis, market research, industrial retail and decision support. Mining association rules is the core task of numerous data mining techniques. As the amount of data increases, designing an efficient mining algorithm becomes increasingly urgent; accordingly, two of the main issues concerning data mining are therefore studied extensively herein. One is the design of algorithms for mining rules or patterns. The other is the design of algorithms to update and maintain rules, called incremental mining. The most celebrated algorithm of the first type is the Apriori [3, 4] algorithm. The Apriori algorithm solves two Figure 1. Each item has an individual exhibition period In the real world where large amounts of data grow steadily, some old association rules can become useless, and new databases may give rise to some implicitly valid patterns or rules. Hence, updating rules or patterns is also important. The FUP algorithm is well known in related to 1 Proceedings of the 15th International Workshop on Research Issues in Data Engineering: Stream Data Mining and Applications (RIDE-SDMA’05) 1097-8585/05 $20.00 © 2005 IEEE confidence is expressed in the form confidence(X Ÿ Y) = support(X  Y)/support(X). Given the user-assigned minimum support (minSup) and minimum confidence (minConf) thresholds for the transaction database DB, the mining of association rules is to find all rules whose support and the confidence, in which are greater than the two respective minimum thresholds. An itemset is called a frequent itemset when its support is no less than the minSup threshold; otherwise, it is an infrequent itemset. this issue [8]. A simple method for solving the updating problem is to reapply the mining algorithm to the entire database, but this approach is time-consuming. The FUP algorithm reuses information from old frequent itemsets to improve its performance. Several other approaches to incremental mining have been proposed [5, 9, 11, 13, 14, 15, 17, 19, 20]. Although many mining techniques for discovering frequent itemsets and associations have been presented, the process of updating frequent itemsets remains troublesome for incremental databases. The mining of incremental databases is more complicated than the mining of static transaction databases, and may lead to some severe problems, such as the combination of frequent itemsets occurrence counts in the original database with the new transaction database, or the rescanning of the original database to check whether the itemsets remain frequent while new transactions are added. Earlier incremental algorithms have focused on reducing the number of scanning on original database while it is updated. However, they require the original database to be rescanned at least once in many situations. This work presents a novel algorithm NFUP for incremental mining, which is based on FUP. This algorithm can discover latest rules and does not need to rescan the original database. This work focuses on the generation of frequent itemsets in incremental publication-like database. The rest of this paper is organized as follows. Section 2 introduces some work on association rules. Then, Section 3 describes the proposed method (NFUP). The experimental results of NFUP will be presented in Section 4. Conclusions are finally drawn in Section 5. 2.1 Apriori Algorithm The Apriori algorithm concentrates primarily on the discovery of frequent itemsets according to a user-defined minSup [4]. The algorithm relies on the fact that an itemset could be frequent only when each of its subset is frequent; otherwise, the itemset is infrequent. In the first pass, the Apriori algorithm constructs and counts all 1-itemsets. (A k-itemset is an itemset that includes k items.) After it has found all frequent 1-itemsets, the algorithm joins the frequent 1-itemsets with each other to form candidate 2-itemsets. Apriori scans the transaction database and counts the candidate 2-itemsets to determine which of the 2-itemsets are frequent. The other passes are made accordingly. Frequent (k - 1)-itemsets are joined to form k-itemsets whose first k-1 items are identical. If k t 3, Apriori prunes some of the k-itemsets; of these, (k – 1)-itemsets have at least one infrequent subset. All remaining k-itemsets constitute candidate k-itemsets. The process is reiterated until no more candidates can be generated. Example 2.1 Consider the database presented in Table 1 with a minimum support requirement is 50%. The database includes 11 transactions. Accordingly, the supports of the frequent itemsets are at least six. The first column “TID” includes the unique identifier of each transaction, and the “Items” column lists the set of items of each transaction. Let Ck be the set of candidate k-itemsets and Fk be the set of frequent k-itemsets. In the first pass, the database is scanned to count C1. If the support count of a candidate exceeds or equals six, then the candidate is added to F1. The outcome is shown in Figure 2. Then, F1 f F1 forms C2 (Apriori-gen function is used to generate C2 [4]). After the database has been scanned for a second time, Apriori examines which itemset of C2 exceeds the predetermined threshold. Moreover, C3 is generated from F2 as follows. Figure 2 presents two frequent 2-itemsets with identical first item, such as {BC} and {BE}. Then, Apriori tests whether the 2-itemset {CE} is frequent. Since {CE} is a frequent itemset, all the subsets of {BCE} are frequent. Thus, {BCE} is a candidate 3-itemset, or {BCE} must be pruned. Apriori stops to look for frequent itemsets when no candidate 4-itemset can be joined from F3. Apriori scans the database k times when candidate k-itemsets are generated. 2. Related Work In 1993, Agrawal et al. first defined the mining of association rules in databases [3]. They considered the example following example; 60% of transactions in which bread is purchased are also transactions in which milk is purchased. The formal statement is as follows [3]. Let I = {i1, i2,… , im} represent the set of literals, called items. The symbol T represents an arbitrary transaction, which is a set of items (itemset) such that T Ž I. Each transaction has a unique identifier, TID. Let DB be a database of transactions. Assume X is an itemset; a transaction T contains X if and only if X Ž T. An association rule applies in the form X Ÿ Y, where X Ž I, Y Ž I and X  Y= I (For example, I = {ABCDE}, X = {AC}, Y = {BE}). An association rule X Ÿ Y has two properties, support and confidence. When s% of transactions in DB contain X  Y, the support of the rule X Ÿ Y is s%. If some of the transactions in DB contain X and, and c% also contain Y, then the confidence in the rule X Ÿ Y is c%. In general, the 2 Proceedings of the 15th International Workshop on Research Issues in Data Engineering: Stream Data Mining and Applications (RIDE-SDMA’05) 1097-8585/05 $20.00 © 2005 IEEE rescanned. The process is reiterated until all frequent itemsets have been found. In the worst case, FUP does not reduce the number of the original database must be scanned. Table 1. An example of a transaction database TID 001 002 003 004 005 006 007 008 009 010 011 Pass 1 Scan DB ==> Pass 2 F1 f F1 ==> C2 {AB} {AC} {AE} {BC} {BE} {CE} Scan DB ==> Items ACDE ACD BCE ABCE ABE BCE ABE BCDE ABCD CEF ABCF Table 2. Four scenarios associated with an itemset in DB+ db DB Frequent itemset Infrequent itemset C1 Count F1 Count {A} 7 {A} 7 {B} 8 {B} 8 {C} 9 ==> {C} 9 {D} 4 {E} 8 {E} 8 {F} 2 f F2 & Prune ==> Case 1: Frequent Case 3: Case 2: Case 4: Infrequent In 1997, Cheung et al. described the FUP2 algorithm, which is a more general incremental technique than FUP. FUP2 is efficient not only on developing of a database but also on trimming data [9]. Tomas et al. proposed another method to accelerate the incremental mining by maintaining the negative border [19]. In 1999, Ayan et al. proposed the UWEP (Update With Early Pruning) method that employs a dynamic look-ahead strategy to update existing frequent itemsets for detecting and removing itemsets that are infrequent in the updated database [5]. In 2001, Lee et al. proposed the SWF approach [13]. SWF partitions databases into several partitions, and applies a filtering threshold in each partition to generate candidate itemsets. In 2002, Veloso et al. described the ZigZag algorithm which uses tidlist and computes maximal frequent itemsets in the updated database to avoid the generation of many unnecessary candidates [20]. C2 Count F2 Count {AB} 5 {BC} 6 {AC} 5 {BE} 6 {AE} 4 ==> {CE} 6 {BC} 6 {BE} 6 {CE} 6 Scan C3 C3 Count {BCE} DB {BCE} 4 ==> ==> Infrequent itemset 2.3 Other Incremental Algorithms Pass 3 F2 Frequent itemset F3 Count {} Figure 2. Application of Apriori algorithm 3. New Fast Update Method (NFUP) The key idea behind of previous incremental mining techniques is to reduce the number of times that databases need to be scanned. Although those techniques may avoid some unnecessary scanning, they do rescan the original database. The original database is normally much larger than the incremental database. Therefore, scanning the original database is time-consuming. This study proposes a new fast update algorithm (NFUP) for incremental mining of association rules. NFUP does not require the rescanning of the original database to detect new frequent itemsets or delete invalidate itemsets. 2.2 Fast Update Algorithm (FUP) After a database has been updated, some existing rules are no longer important and new rules may be introduced. In 1996, Cheung et al. proposed the FUP algorithm to efficiently generate associations in the updated database [8]. The FUP algorithm relies on Apriori and considers only these newly added transactions. Let db be a set of new transactions and DB+ be the updated database (including all transactions of DB and db). An itemset X is either frequent or infrequent in DB or db. Therefore, X has four possibilities, as shown in Table 2. In the first pass, FUP scans db to obtain the occurrence count of each 1-itemset. Since the occurrence counts of Fk in DB are known in advance, the total occurrence count of arbitrary X is easily calculated if X is in Case 2. If X is unfortunately in Case 3, DB must be rescanned. Similarly, the next pass scans db to count the candidate 2-itemsets of db. If necessary, DB is 3.1 NFUP Algorithm FUP rescans the original database when at least one candidate is in Case 3. In many situations, new information is more important than old information, such as in publication database, stock transactions, grocery markets, 3 Proceedings of the 15th International Workshop on Research Issues in Data Engineering: Stream Data Mining and Applications (RIDE-SDMA’05) 1097-8585/05 $20.00 © 2005 IEEE or web-log records. Consequently, a frequent itemset in the incremental database is also important even if it is infrequent in the updated database. To mine new interesting rules in updated database, NFUP partitions the incremental database logically according to unit time interval (month, quarter or year, for example). For each item, assume that the ending time of exhibition period is identical. NFUP progressively accumulates the occurrence count of each candidate according to the partitioning characteristics. The latest information is at the last partition of incremental database. Therefore, NFUP scans each partition backward, namely, the last partition is scanned first and the first partition is scanned last. As in the preceding section, the original transaction database is denoted as DB, where db indicates the incremental portion, and DB+ signifies the updated database. The frequent set of itemsets of DB is known in advance. The new transaction database db includes n unit time intervals. Logically, db can be divided into n portions and each portion is called a partition (db = P1  P2  , ...,  Pn where Pn denotes the partition n). Let dbm, n represent the continuous time interval from partition Pm to partition Pn, where n t m t 1 and n  N. Namely, dbm, n = Pm  Pm+1  , ...,  Pn-1  Pn. The NFUP algorithm is an Apriori-like algorithm. The final set of frequent itemsets consists of the three following types. (1) Į set: frequent itemsets in DB+, (2) ȕ set: frequent itemsets in dbm, n (m d n), but infrequent in dbm-1, n, and (3) r set: frequent itemsets in dbm, m, but infrequent in dbm+1, n. Figure 3. Process of NFUP for Pm The pseudo-code of NFUP algorithm is presented as follows. Input: (1) DB+: updated database that contain DB (original database) with size |DB| and the incremental n database db1,n with size |db1,n| = | ¦m 1 Pm |, (2) Fk: set of all frequent k-itemsets in DB, where k = 1, 2,…, h, and (3) s: minSup. Output: (1) FĮ (Į set): frequent itemsets in DB+, (2) Fȕ (ȕ set): frequent itemsets in dbm, n (m d n), but infrequent in dbm-1, n or infrequent in DB+ (if m = 1), and (3) Fr (r set): frequent itemsets in dbm, m, but infrequent in dbm+1, m+1. Procedure: // Cmk is the candidate k-itemsets in partition m // FĮk is the set with k items in FĮ; Fȕk is the set with k items in Fȕ; Frk is the set with k items in Fr; // FDB is the set of frequent itemsets in DB 01 FĮ := I ; Fȕ := I ; Fr := I ; 02 for m := n to 1 { 03 k:=1; 04 SubProcedure(); 05 for k := 2 to h { 06 Cmk := Apriori-gen(FĮk-1); 07 SubProcedure(); 08 } 09 } 10 forall X  FĮ  FDB { 11 if X  FĮ && X  FDB { 12 F(X).start = 0 ; 13 F(X).count += FDB(X).count; } { 14 elseif X  FĮ && X  FDB 15 F(X).type = ȕ; } 16 elseif X  FDB && X  FĮ  Fȕ  Fr { 17 F(X).type = r; } 18 } 19 return FĮ, Fȕ, and Fr; For dbn, n (Pn), the process starts at 1-itemsets. Each candidate or frequent itemset has three attributes. (1) X.count: includes the occurrence count in current partition, (2) X.start: includes the partition number of the corresponding starting partition when X becomes an element of frequent set, and (3) X.type: denotes one of the three types Į, ȕ, and r. In the beginning, set Į, set ȕ, and set r are empty. After Pn has been scanned, all frequent 1-itemsets are added into the Į set. Each frequent 1-itemset is joined to form 2-itemset candidates. In Pn, the process is performed like that of Apriori. NFUP is applied to the next partition Pn-1 whenever no more candidate k-itemsets can be generated in Pn. The occurrence count of each candidate in Pn-1 is known after Pn-1 is scanned. In each partition, NFUP determines which candidate k-itemset will become an element of Į, ȕ or r set and identifies from which partition the k-itemset becomes frequent. After P1 is scanned, the occurrence count is accumulated with that of DB. Figure 3 graphically depicts NFUP process for Pm, where FĮ is the Į set, Fȕ is the ȕ set, and Fr is the r set. 4 Proceedings of the 15th International Workshop on Research Issues in Data Engineering: Stream Data Mining and Applications (RIDE-SDMA’05) 1097-8585/05 $20.00 © 2005 IEEE to be scanned. In the beginning, these frequent k-itemsets in P2 belong to the Į set. Table 5 lists the three types of frequent set. The column “Start” states the identity of the start partition. After P1 is scanned, the Į set consists of five entries. In Į set, the value of start partition of each frequent k-itemset is modified to be one. Four k-itemsets are removed to the ȕ set because their total occurrence counts are less than the threshold (6 * 50% = 3). Furthermore, the three itemsets {E}, {BE}, and {CE} are presented in r set. Although {BE} is frequent in db1, 2, it is infrequent in P2, as marked by “*”. Finally, NFUP adds the occurrence counts of frequent itemsets in DB to the corresponding frequent itemsets of the Į set. In Table 5, the final Į set remains three entries {A}, {B}, and {C}. The ȕ set and r set increase two and one entries, respectively. In Line 1, Į, ȕ and r sets are initialized to empty. In Lines 4 and 7, SubProcedure() is applied to scan a portion of db and to compute the support number of each candidate. At the same time, it determines which candidate should be added to a proper frequent set or be ignored. The Apriori-gen function takes frequent (k-1)-itemsets to generate k-itemset candidates. The prune step is included in the Apriori-gen function. Some of the k-itemsets are deleted; of these, at least one (k-1) sub-itemset is not in FĮk-1. From Line 10 to Line 18, the final support value of each frequent itemset of Į set needs to be added its occurrence count in DB. Otherwise, they are the elements of ȕ set. The pseudo-code of SubProcedure() is presented as follows. Table 3. Transaction database SubProcedure(): // the k-th pass in each partition 01 if Cmk Ž I { break; } 02 if m == n { 03 forall X  Cmk { F(X).count = 0; } } 04 forall X  Cmk { X.count :=0; } 05 forall T  Pm { // scan Pm , T:transaction 06 forall X  (subset of T) { 07 if X  Cmk { X.count++; } } 08 } 09 forall X  Cmk { 10 if X  FĮk { 11 if X.count t s*|Pm| { 12 F(X).start = m ; F(X).count += X.count; } 13 else { 14 if F.count + F(X).count t s*|dbm,n| { 15 F(X).count += X.count; } 16 else { 17 FĮk := FĮk - {X}; Fȕk := Fȕk  {X}; 18 F(X).count += X.count; 19 F(X).type := ȕ; } } } 20 elseif X  Cmk – FĮk – Fȕk – Frk{ 21 if X.count t s*|Pm| { 22 F(X).count := X.count; 23 if m == n { F(X).type := Į ;} 24 else { Frk := Frk  {X}; F(X).type := r ;} 25 } } 26 } Date Partition TID Transaction DB 001 A C D E 1999 002 A C D | 003 B C E 2001 004 A B C E 005 A B E 2002 P1 006 B C E 007 A B E 008 B C D E 2003 P2 009 A B C D 010 C E F 011 A B C F P Table 4. Frequent itemsets in each partition P2 P1 DB Itemset Count Itemset Count Itemset Count {A} 2 {B} 3 {A} 4 {B} 2 {C} 2 {B} 3 {C} 3 {E} 3 {C} 4 {F} 2 {BC} 2 {E} 4 {AB} 2 {BE} 3 {AC} 3 {AC} 2 {CE} 2 {AE} 3 {BC} 2 {BCE} 2 {BE} 3 {CF} 2 {CE} 3 {ABC} 2 P As shown in Table 5 from 1999 to 2003, the three publications or products ({A}, {B} and {C}) are very popular because their start partitions are zero. {AB} and {BC} are the two elements of the ȕ set and P1 is their start partition. Thus, from 2002 to 2003, the two combinations of products are interesting. {AE} is in the r set and the start partition is zero. Hence, {AE} is very popular from 1999 to 2001. However, {AE} is no longer interesting from 2002 to 2003. The itemset {E} is frequent in traditional incremental rules mining such as FUP, while {E} is in the r set of the mining result of NFUP. Although the occurrence Example 3.1 Consider the transaction database presented in Table 3 with a minimum support requirement is 50%. The original database contains five transactions and that six incremental transactions are divided into two portions {P1, P2}. DB corresponds to the time granularity from 1999 to 2001. P1 and P2 correspond to the time granularities 2002 and 2003, respectively. All frequent itemsets of DB are known in advance, and presented in Table 4. Initially, the three types of frequent set are null. Without loss of generality, suppose DB is the partition zero (P0). All the frequent k-itemsets in Pm are also list in Table 4. P2 is first 5 Proceedings of the 15th International Workshop on Research Issues in Data Engineering: Stream Data Mining and Applications (RIDE-SDMA’05) 1097-8585/05 $20.00 © 2005 IEEE count of {E} is eight in DB+, {E} is no longer frequent in the year 2003. 100,000, P = 1 to 4, |T| = 10, |I| = 4, |L|=2000, and N = 1000. The notation Tx.Iy.Dz.dm.Pn denotes an updated database DB+, where |T| = x, |I| = y, |D| = z, |d| = m, and P = n. Figure 4 shows the running time for P = 1, 2 and 4. The minSup threshold is decreased from 1.2% to 0.2%. NFUP has the best performance when the partition number of db is one. Table 5. Frequent itemsets generated incrementally by NFUP After P2 is scanned After P1 is scanned Final frequent sets Į set Start Count Į set Start Count Į set Start Count {A} 2 2 {A} 1 3 {A} 0 7 {B} 2 2 {B} 1 5 {B} 0 8 {C} 2 3 {C} 1 5 {C} 0 9 {F} 2 2 {AB} 1 3 {AB} 2 2 {BC} 1 4 ȕ set Start Count {AC} 2 2 {F} 2 2 {BC} 2 2 ȕ set Start Count {AB} 1 3 {CF} 2 2 {F} 2 2 {AC} 2 2 {ABC} 2 2 {AC} 2 2 {BC} 1 4 {CF} 2 2 {CF} 2 2 {ABC} 2 2 {ABC} 2 2 r set Start Count {E} 1 3 *{BE} 1 3 {CE} 1 2 Table 6. Parameters |D| Number of transactions in DB |d| Number of transactions in db P Partition number of the incremental db |T| Mean size of the transactions |I| Mean size of the maximal potentially frequent itemsets |L| Number of maximal potentially frequent itemsets N Number of items r set Start Count {E} 1 3 {AE} 0 3 {BE} 1 3 {CE} 1 2 To test the scalability with the number of transactions of db, the number of partitions of db is set to 2. Figure 5 presents the results. Consider the two minimum support thresholds 0.2% and 0.4%, the running time slightly increases with the growth of db’s size. Thus, NFUP shows good scalability. Figure 6 shows the scalability with the number of transactions of DB, where the incremental database is also divided into two partitions. The curves of 0.2% and 0.4% minimum support thresholds are very flat. Therefore, the running time of NFUP is irrelevant to the number of transactions of DB. Running time (sec). NFUP needs not rescan the original database since the Į set is frequent in the updated database DB+, and the ȕ set provides important rules in dbm,n. Determining all frequent itemsets in DB+ as Apriori or FUP, it requires the rescanning of the original database only once to check the ȕ set and r set. However, this rescanning phase is unnecessary because all frequent itemsets in DB+ are the subset of Į  ȕ  r. Furthermore, all the itemsets contained in ȕ set or r set are interesting. To determine all frequent itemsets in DB+ as Apriori or FUP, the important rule could be deleted by pruning some frequent itemsets from the ȕ set or r set. The set (Į  ȕ  r) is the superset of the mining result of Apriori in DB+. The reason is that if DB is divided into n partitions, then the frequent itemset X must appear as a frequent itemset in least one of the n partitions [18]. T10.I4.D100k.d100k.Pn 40 30 n=1 20 n=2 10 n=4 0 0.2 4. Experimental Results All the experiments were performed on a 1.5GHz Pentium IV PC with 640 MB of main memory, running under Windows 2000 professional. The algorithm was coded in Visual C++ 6.0. The synthetic datasets employed in our experiments are generated by using the same technique introduced in [4]. Table 6 is the parameters of the synthetic data generation program. We generate the transaction database DB+ with size |DB+|, where the first |DB| is the original database and the next |db| (|DB+| - |DB|) is the incremental portion. The result is shown in Figure 4, where |D| = 100,000, |d| = 0.4 0.6 0.8 1 1.2 Minimum Suppport(%) Figure 4. Running time of NFUP for n = 1, 2 and 4 6 Proceedings of the 15th International Workshop on Research Issues in Data Engineering: Stream Data Mining and Applications (RIDE-SDMA’05) 1097-8585/05 $20.00 © 2005 IEEE Running tine (sec). References T10.I4.D100k.dm .P2 25 [1] R. C. Agarwal, C. C. Aggarwal, and V. V. V. 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Joint 9th IFSA World Congress and 20th NAFIPS Intl. Conf., Vancouver, Canada, pp. 441-446, Jul. 2001. [16] J. S. Park, M. S. Chen, and P. S. Yu, “An effective hash-based algorithm for mining association rules,” In Proc. 20 15 0.20% 10 0.40% 5 0 20 40 60 80 100 |db | transaction number (k ) Figure 5. Scalability with the transaction number of db T10.I4.Dz .d100k.P2 Running time(sec). 25 20 15 0.20% 10 0.40% 5 0 100 200 400 600 800 1000 |DB | transaction number (k ) Figure 6. Scalability with the transaction number of DB 5. Conclusions In the real world, databases are periodically and continually updated. Therefore, mining must be repeated. Valid patterns and rules must to be efficiently generated. Incremental mining must usually involve the original database and the new added transactions. Scanning the original database is very expensive, so the proposed method outperforms others by avoiding the rescanning of the original database. This investigation has presented a new method, NFUP, for incremental mining. NFUP does not require the rescanning of the original database and can determine new frequent itemsets at the latest time intervals. The proposed method uses information available from a following partition to avoid the rescanning of the original database; it requires only the incremental database to be scanned. In reality, the transaction number of the incremental database is very small in contrast to the original database. The running time of NFUP rises almost in direct proportion with the transaction number of the incremental database. Accordingly, NFUP is suited frequently updated databases. In the future, the authors will consider the extension of the NFUP algorithm to sequence rules. 7 Proceedings of the 15th International Workshop on Research Issues in Data Engineering: Stream Data Mining and Applications (RIDE-SDMA’05) 1097-8585/05 $20.00 © 2005 IEEE 1995 ACM-SIGMOD Intl. Conf. on Management of Data, San Jose, CA, pp. 175-186, May 1995. [17] N. L. Sarda and N. V. Srinivas, “An adaptive algorithm for incremental mining of association rules,” In Proc. 9th Intl. Workshop on Database and Expert Systems Applications, Vienna, Austria, pp. 240-245, Aug. 1998. [18] A. Savasere, E. Omiecinski, and S. Navathe, “An efficient algorithm for mining association rules in large databases,” In Proc. 21st Conf. on Very Large Data Bases, Zurich, Switzerland, pp. 432-444, Sep. 1995. [19] S. Thomas, S. Bodagala, K. Alsabti, and S. Ranka, “An efficient algorithm for the incremental updating of association rules in large database,” In Proc. 3rd Intl. Conf. on Data Mining and Knowledge Discovery, Newport Beach, CA, pp. 263-266, Aug. 1997. [20] A. A. Veloso, W. Meira Jr., M. B. de Carvalho, B. Pôssas, S. Parthasarathy, and M. J. Zaki, “Mining frequent itemsets in evolving databases,” In Proc. 2nd SIAM Intl. Conf. on Data Mining, Arlington, VA, Apr. 2002. 8 Proceedings of the 15th International Workshop on Research Issues in Data Engineering: Stream Data Mining and Applications (RIDE-SDMA’05) 1097-8585/05 $20.00 © 2005 IEEE View publication stats